TABLE OF CONTENTS The term tomography refers to the general class of devices and procedures for producing two-dimensional (2D) cross-sectional images of a three-dimensional (3D) object. Tomographic systems make it possible to image the internal structure of objects in a non-invasive and non-destructive manner. By far the best known application is the computer assisted tomography (CAT or simply CT) scanner for x-ray imaging of the human body. Other medical imaging devices, including PET (positron emission tomography), SPECT (single photon emission computed tomography) and MRI (magnetic resonance imaging) systems, also make use of tomographic principles. Outside of the biomedical realm, tomography is used in diverse applications such as microscopy, non-destructive testing, radar imaging, geophysical imaging and radio astronomy.
We will restrict our attention here to image reconstruction methods for x-ray CT, PET and SPECT. In all three modalities the data can be modeled as a collection of line integrals of the unknown image. Many of the methods described here can also be applied to other tomographic problems. However, the reader should refer to Chapter 3.6 for a more general treatment of image reconstruction in the context of ill-posed inverse problems.
We describe 2D image reconstruction from parallel and fan-beam projections and 3D reconstruction from sets of 2D projections. Algorithms derived from the analytic relationships between functions and their line integrals, the so called "direct methods" are described in Sections 3-5. In Section 6 we describe the class of "iterative methods" that...
